Related papers: Symmetry invariance for adapting biological system…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Embodied systems experience the world as 'a symphony of flows': a combination of many continuous streams of sensory input coupled to self-motion, interwoven with the dynamics of external objects. These streams obey smooth,…
Cross-domain few-shot learning (CD-FSL) requires models to generalize from limited labeled samples under significant distribution shifts. While recent methods enhance adaptability through lightweight task-specific modules, they operate…
Evolution in changing environments is an important, but little studied aspect of the theory of evolution. The idea of adaptive walks in fitness landscapes has triggered a vast amount of research and has led to many important insights about…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
Leveraging the intrinsic symmetries in data for clear and efficient analysis is an important theme in signal processing and other data-driven sciences. A basic example of this is the ubiquity of the discrete Fourier transform which arises…
Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
Learning to predict agent motions with relationship reasoning is important for many applications. In motion prediction tasks, maintaining motion equivariance under Euclidean geometric transformations and invariance of agent interaction is a…
Possibility to establish macroscopic phenomenological theory for biological systems, akin to the akin to the well-established framework of thermodynamics, is briefly reviewed. We introduce the concept of an evolutionary fluctuation-response…
The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are…
The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…
Using local density correlation functions for a one-dimensional spin system, we introduce a correlation function difference (CFD) which compares correlations on a given site between a full system of size $L$ and its restriction to $\ell<L$…
Living systems need to be highly responsive, and also to keep fluctuations low. These goals are incompatible in equilibrium systems due to the Fluctuation Dissipation Theorem (FDT). Here, we show that biological sensory systems, driven far…
Understanding effect modification -- how treatment effects vary across subpopulations -- is practically important in observational studies, as it helps identify which subgroups are likely to benefit from a given treatment. In this paper, we…
A system consisting of a doubly clamped beam with an attached body (slider) free to move along the beam has been studied recently by multiple research groups. Under harmonic base excitation, the system has the capacity to passively adapt…
Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory…
We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…
Group living animals form aggregations and flocks that remain cohesive in spite of internal movements of individuals. This is possible because individual group members repeatedly adjust their position and motion in response to the position…
By reviewing the application of the renormalization group to different theoretical problems, we emphasize the role played by the general symmetry properties in identifying the relevant running variables describing the behavior of a given…